Question: $f(x) = \dfrac{ x + 6 }{ ( x + 6 )( x - 2 ) }$ What is the domain of the real-valued function $f(x)$ ?
Solution: $f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-6$ or $x=2$ So we know that $x \neq -6$ and $x \neq 2$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-6, \,x \neq2\, \}$.